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Search: id:A110835
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| A110835 |
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Smallest m > 0 such that there are no primes between n*m and n*(m+1) inclusive. |
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+0
1
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| 8, 4, 8, 6, 18, 15, 17, 25, 13, 20, 29, 44, 87, 81, 35, 83, 79, 74, 70, 67, 118, 330, 58, 223, 172, 229, 179, 471, 292, 360, 506, 367, 586, 577, 645, 545, 424, 743, 503, 637, 766, 467, 937, 579, 698, 683, 542, 1443, 641, 628, 616, 604, 2026, 1661, 571, 1834, 551
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Suggested by Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2. If a(n)>=n+2, it implies that there is always a prime between n^2 and n*(n+1) and another between n*(n+1) and (n+1)^2. Note that the "inclusive" condition for the range affects only n=1. The value of a(1) would be 1 or 3 if this condition was taken to be exclusive or semi-inclusive, respectively.
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EXAMPLE
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a(2)=4 because the primes 3,5 and 7 are in range 2m to 2m+2 for m from 1 to 3, but 8, 9 and 10 are all composite.
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PROGRAM
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(PARI) a(n)=local(m); m=1; while(nextprime(n*m)<=n*(m+1), m=m+1); m
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CROSSREFS
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See A014085 for primes between squares.
Sequence in context: A021545 A141614 A010524 this_sequence A087015 A124012 A000803
Adjacent sequences: A110832 A110833 A110834 this_sequence A110836 A110837 A110838
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KEYWORD
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easy,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Sep 16 2005
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